I do something similar to my door. Instead of a rubber flap I use several layers of plastic that have been sliced into strips, think of a loading dock in the winter. That's what I modeled mine after.
I only close my door in a blizzard or when it's going to be a super cold night. The rest of the time it's just covered with the plastic strips.
I take this plastic down during the warmer months, so every fall I have to "retrain" them to use it. The way I train them is to install the plastic(rubber flap in your case) so it's only extending 1/3rd down over the opening. I give them a couple days to get used to ducking under this then I lower it some more and give them a couple days to deal with it. After maybe a week or so of slowly increasing the amount of the opening that is covered, I end up with the plastic extending all the way down over the opening and the chickens just push through it without hesitation.
Maybe it would be helpful if you cut your flap into strips, this would make it give easier when a chicken tries to poke it's head through.